Question: Express this quotient in scientific notation: ${\frac{2.250\times 10^{5}} {5.0\times 10^{-1}}}$
Explanation: Start by collecting like terms together. $= {\frac{2.250} {5.0}} \times{\frac{10^{5}} {10^{-1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.45 \times 10^{5\,-\,-1}$ $= 0.45 \times 10^{6}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.45$ is the same as $4.50 \div 10$ , or $4.50 \times 10^{-1}$ $ = {4.50 \times 10^{-1}} \times 10^{6} $ $= 4.50\times 10^{5}$